# The Meixner Process

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This Demonstration shows a path of the (extended) Meixner process with four parameters and a cross-sectional ("marginal") density function of the process at a chosen moment in time. The kurtosis and skewness of the density at the given time are also displayed. The Meixner process is a pure-jump Lévy process with semi-heavy tails, which has been used successfully for stock price modelling and valuing derivative instruments. The Demonstration makes use of *Mathematica 8*'s ability to generate random variates when an explicit formula for the probability density function is given.

Contributed by: Andrzej Kozlowski (January 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Meixner process is a three-parameter pure jump Lévy process that was introduced in [1] and applied to finance in [2]. As with other similar processes, one can add a "drift" parameter, creating a four-parameter process particularly convenient for pricing derivative instruments. The process originated in the theory of orthogonal polynomials. It is a pure jump Lévy process (i.e. it has no continuous component) and was defined by explicitly giving its density function, which plays the central role in this Demonstration.

References

[1] W. Schoutens and J. L. Teugels, "Lévy Processes, Polynomials and Martingales," *Communications in Statistics: Stochastic Models*,* *14, 1998 pp. 335–349.

[2] W. Schoutens, *Lévy Processes in Finance: Pricing Financial Derivatives*, New York: John Wiley & Sons, 2003.

## Permanent Citation

"The Meixner Process"

http://demonstrations.wolfram.com/TheMeixnerProcess/

Wolfram Demonstrations Project

Published: January 16 2012